With the advances in photolithography and the rapid development of the semiconductor industry, the following four basic metrics have been developed for measuring the performance of photolithography equipment: critical dimension (CD) uniformity, focus, overlay and throughput. In order to enhance the CD uniformity, increases in horizontal positioning accuracy of the wafer or mask stage are required. In order to enhance the focus accuracy, increases in vertical positioning accuracy of the wafer or mask stage are required. In order to obtain higher overlay accuracy, a photolithography tool has to improve the internal model of its wafer or mask stage for better dynamic positioning performance. In addition, in order to meet the necessary requirement for an increasing throughput of photolithography equipment, the wafer or mask stage is further required to be capable of fast movement, quick start-up and shutdown. The high-speed, high-acceleration and high-positioning-performance requirements on photolithography equipment conflict with one another, because a higher scanning speed requires a more powerful motor capable of long path movement at a higher speed with multiple DoFs for lithographic exposure and alignment. Linear motors are transmission devices that can directly convert electric power into linear mechanical movement without the aid of any intermediate conversion mechanism. They are advantageous over rotary motors in terms of structural simplicity, positioning accuracy, transmission efficiency, etc. and have therefore been widely used in high-precision positioning platforms for photolithography equipment.
As shown in FIGS. 1 and 2, a conventional linear motor generally includes a Halbach magnet array 101 and a group of three-phase coils 102a, 102b, 102c. Upon the three-phase coils 102a, 102b, 102c energized with respective three-phase electrical currents, the Halbach magnet array 101 works with the three-phase coils 102a, 102b, 102c to produce actuating forces. The mechanism is that, assuming the currents introduced in the three-phase coils 102a, 102b, 102c are respectively ia, ib, ic, the linear motor is displaced by a distance of y in the Y-direction, a pole pitch of the permanent magnets is τ, and every two adjacent coils are spaced apart by 4τ/3, flux densities Bya, Byb, Byc of a magnetic field created by the three-phase coils 102a, 102b, 102c in the Y-direction and flux densities thereof Bza, Bzb, Bzc in the Z-direction are given as:
                    {                                                            Bya                =                                                      B                    ^                                    ⁢                                                                          ⁢                                      y                    ·                                          cos                      ⁡                                              (                                                                              π                            ⁢                                                                                                                  ⁢                            y                                                    τ                                                )                                                                                                                                                                    Byb                =                                                      B                    ^                                    ⁢                                                                          ⁢                                      y                    ·                                          cos                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    4                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                                                                                                                    Byc                =                                                      B                    ^                                    ⁢                                                                          ⁢                                      y                    ·                                          cos                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    8                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                                                                                                    (        1        )                                {                                                            Bza                =                                                      -                                          B                      ^                                                        ⁢                                                                          ⁢                                      z                    ·                                          sin                      ⁡                                              (                                                                              π                            ⁢                                                                                                                  ⁢                            y                                                    τ                                                )                                                                                                                                                                    Bzb                =                                                      -                                          B                      ^                                                        ⁢                                                                          ⁢                                      z                    ·                                          sin                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    4                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                                                                                                                    Bzc                =                                                      -                                          B                      ^                                                        ⁢                                                                          ⁢                                      z                    ·                                          sin                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    8                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                                                                                                    (        2        )            
where, {circumflex over (B)}y represents Y-directional flux density amplitude of the Halbach magnet array 101, and {circumflex over (B)}z denotes Z-directional flux density amplitude of the Halbach magnet array 101.
According to a vector control technique for three-phase motors, control is accomplished by D-Q decomposition, wherein vertical and horizontal (i.e., in the X-Y plane) forces are controlled by d- and q-axis currents, and the currents ia, ib, is for the three-phase coils 102a, 102b, 102c can be expressed as a function of the d- and q-axis currents id and iq:
                    {                                                            ia                =                                                      iq                    ·                                          cos                      ⁡                                              (                                                                              π                            ⁢                                                                                                                  ⁢                            y                                                    τ                                                )                                                                              -                                      id                    ·                                          sin                      ⁡                                              (                                                                              π                            ⁢                                                                                                                  ⁢                            y                                                    τ                                                )                                                                                                                                                                    ib                =                                                      iq                    ·                                          cos                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    4                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                              -                                      id                    ·                                          sin                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    4                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                                                                                                                    ic                =                                                      iq                    ·                                          cos                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    8                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                              -                                      id                    ·                                          sin                      ⁡                                              (                                                                                                            π                              ⁢                                                                                                                          ⁢                              y                                                        τ                                                    +                                                                                    8                              ⁢                                                                                                                          ⁢                              π                                                        3                                                                          )                                                                                                                                                    (        3        )            
Therefore, the Y- and Z-forces Fy, Fz generated by the linear motor are:
                              [                                                    Fy                                                                    Fz                                              ]                =                              [                                                            Bya                                                  Byb                                                  Byc                                                                              Bza                                                  Bzb                                                  Bzc                                                      ]                    ×                      [                                                            ia                                                                              ib                                                                              ic                                                      ]                                              (        4        )            
The Y-directional horizontal force Fy and the Z-directional vertical force Fz make the linear motor able to move in the Y- and Z-directions, respectively. However, during the exposure and alignment, the photolithography equipment needs to move with six DoFs, i.e., the freedom of translational movement in the X-, Y- and Z-directions and slight rotational movement about the X-, Y- and Z-directions. Therefore, the traditional linear motor cannot meet the requirements of high-precision positioning.
In order to solve this problem, there has been also proposed in the prior art a linear motor incorporating four instances of the conventional Halbach linear motor so that they can cooperate with one another to support six-DoF movement needed by a photolithography platform. However, subject to limitations arising from the layout of magnet arrays, the linear motor has a limited movement path length in the horizontal direction.